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Open-ended, problem-solving maths assignments

New open-ended maths focus in Queensland schools needs students to think differently

Thanks to the spike in anxiety levels of Years 7 to 10 children, many parents are suddenly aware of the shifting school maths curriculum. It’s moving away from:

Clear tasks with a well-defined procedure from start to end, with one expected right-or-wrong answer,

and towards:

More real-life tasks that each student will approach differently, and then justify their conclusions.

This is causing big headaches because neither students nor parents are used to this type of task. Unless students are introduced to expectations and working habits in very early secondary – or better yet, in primary school – they face a painfully radical change in mindset if they are to cope with this style of assessment.

There are things that you can do to help your child face open-ended maths assignments. But first…

What is an open-ended problem?

The task sheets for these open-ended tasks are often convoluted, but to give you an idea, here are some recent examples we’ve seen:

Year 6 – Estimate how many lollies are in this jar in two ways, using measurements and volume calculations; explain which estimate is probably better.

Year 7 – Using area calculations, suggest a shape and layout for a barn in a paddock which allows a tethered goat to reach the most grass.

Year 8 – Redesign your school’s vegetable garden to improve its usability, compare the new and old design using charts to show improvements, and calculate the cost of materials.

Year 10 – Design a skateboard course to meet criteria, using linear, quadratic and simultaneous equations to create an exact plan for the builders.

Year 12 – Analyse the queues at your school canteen, as well as the canteen procedures, and justify suggested improvements to the system using networks and queueing theory.

Students must write a report explaining their interpretation of the problem, the procedure they developed, and why their solution is reasonable.

Of course, mathematical procedures need to be shown, but equations are secondary to analysing, explaining and justifying in words.

Queensland Curriculum and Assessment Authority mandates that schools create maths assessments to be solved like this in Year 11 and 12 mathematics:

Once mastered, this process can be used all through high school to Year 12, and beyond.

What you should do

Some schools have been transitioning students into the ways of thinking and working needed to take on this new kind of assignment.

But even then, the shift has been too sudden for some students who are used to the (unhelpful yet ubiquitous!) idea that maths is about following a pre-set path to come to one conclusion.

These old habits need to be broken. Ease your child’s transition by helping them realise sooner rather than later.

Some critical points to reiterate to your children:

First, understand the whole task. We see that students who don’t “begin with the end in mind” are wasting a lot of time and effort on unnecessary work which won’t translate into a higher mark. In the past, students could step their way through an assignment, section by section, to arrive at the end without ever considering how all the parts relate to each other as a whole. No more!

Pay attention to the details and guides on the task sheet. Information on task sheets is often presented haphazardly, so extract the details and write it in dot points to check off as you go. In lower year-levels, there is often a suggested problem-solving process chart included for students to follow to develop their solution. Also check the marking rubric to see what needs to be included for the teacher to award high marks.

Discuss the task with teachers, family and friends. The more that students explain the task to others, and hear others’ perspectives, the better the path they will develop to their solution. However, even though the task sheets are presented as open-ended, and for students to find their own unique solutions, some teachers have very set ideas about how they want the task done. Ultimately, students must please the person who will mark the work, which means getting feedback from teachers.

Start immediately. These tasks can eat TIME while students figure out how to tackle them, and those who used to be able to leave tasks until the last few days are not finishing these kinds of tasks.

Finish early.Pretend the due date is a week before it actually is so that there is time spare for last-minute changes or additions. FINISH the assignment fully by the DRAFT submission date so that teachers have the opportunity to give feedback on the WHOLE assignment.

Encourage your child to follow this advice from as early as possible.

How ELC can help

We’ve never let the school system dictate what ELC students study session by session. We hit students current school content only when absolutely necessary – conscious that, in the long run, ELC time is far more effectively spent working ahead of school.

We want our students to discuss their tasks with us and present their work for our feedback. But there is not enough time to complete these assignments solely within ELC sessions. So, we give feedback on progress made between sessions, and use most of our precious 75 minutes to continue learning the most important maths content ahead of school.

Our students:

Read the whole task sheet before attending ELC

Start developing ideas and questions immediately

Form an overview of the whole task before beginning

Make as much progress as humanly possible between ELC sessions so that we can give feedback on work done each week.

Bring their ‘finished’ assignment to their ELC session prior to the due date for a final feedback opportunity.

Open-ended maths assessments don’t have to cause the huge stress that some students are feeling. But the right habits do need to be instilled from early on!

If you’re not already any ELC family, talk to us about how ELC can help manage your child’s learning, to prepare them well for a ‘less-stress’ school future, and success beyond.

Dan Blore manages and teaches at Extended Learning Centres. He has spent 11 years’ in education after studying secondary education at University of the Sunshine Coast.
He has taught in Australia and Germany and studied at university in Italy. He most enjoys teaching and studying mathematics and languages, which he focused on at university.